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20 June, 07:14

The data below show the numbers of miles driven to work each day by the employees of a small company 15, 25, 13, 15, 18, 20, 22, 24 The mean of the data is 19 miles. What is the mean absolute deviation of the data?

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  1. 20 June, 07:28
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    The mean absolute deviation is 3.75

    Step-by-step explanation:

    Given:

    Miles travel: 15, 25, 13, 15, 18, 20, 22, 24

    Mean: 19 miles

    Required:

    Mean absolute deviation.

    Given that the mean of the data is known, we start by subtracting the mean from each dataset

    15 - 19 = - 4

    25 - 19 = 6

    13 - 19 = - 6

    15 - 19 = - 4

    18 - 19 = - 1

    20 - 19 = 1

    22 - 19 = 3

    24 - 19 = 5

    Then we calculate the absolute value of each

    |-4| = 4

    |6| = 6

    |-6| = 6

    |-4| = 4

    |-1| = 1

    |1| = 1

    |3| = 3

    |5| = 5

    Add up these result;

    4 + 6 + 6 + 4 + 1 + 1 + 3 + 5

    = 30

    Divide by number of data, to give mean absolute deviation (MAD)

    MAD = 30/8

    MAD = 3.75

    Hence, the mean absolute deviation is 3.75
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